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<<-DOC
Given two binary trees t1 and t2, determine whether the second one is a subtree of the first one.
A subtree for vertex v in binary tree t is a tree consisting of v and all its descendants in t.
Your task is to check whether there is a vertex v in tree t1 such that a subtree for vertex v in t1 equals t2.
Example
For
t1 = {
value: 5,
left: {
value: 10,
left: {
value: 4,
left: {
value: 1,
left: null,
right: null
},
right: {
value: 2,
left: null,
right: null
}
},
right: {
value: 6,
left: null,
right: {
value: -1,
left: null,
right: null
}
}
},
right: {
value: 7,
left: null,
right: null
}
}
and
t2 = {
value: 10,
left: {
value: 4,
left: {
value: 1,
left: null,
right: null
},
right: {
value: 2,
left: null,
right: null
}
},
right: {
value: 6,
left: null,
right: {
value: -1,
left: null,
right: null
}
}
}
the output should be isSubtree(t1, t2) = true.
This is what these trees look like:
t1: t2:
5 10
/ \ / \
10 7 4 6
/ \ / \ \
4 6 1 2 -1
/ \ \
1 2 -1
As you can see, t2 is a subtree of t1 (the vertex in t1 with value 10).
For
t1 = {
value: 5,
left: {
value: 10,
left: {
value: 4,
left: {
value: 1,
left: null,
right: null
},
right: {
value: 2,
left: null,
right: null
}
},
right: {
value: 6,
left: {
value: -1,
left: null,
right: null
},
right: null
}
},
right: {
value: 7,
left: null,
right: null
}
}
and
t2 = {
value: 10,
left: {
value: 4,
left: {
value: 1,
left: null,
right: null
},
right: {
value: 2,
left: null,
right: null
}
},
right: {
value: 6,
left: null,
right: {
value: -1,
left: null,
right: null
}
}
}
the output should be isSubtree(t1, t2) = false.
This is what these trees look like:
t1: t2:
5 10
/ \ / \
10 7 4 6
/ \ / \ \
4 6 1 2 -1
/ \ /
1 2 -1
As you can see, there is no vertex v such that the subtree of t1 for vertex v equals t2.
For
t1 = {
value: 1,
left: {
value: 2,
left: null,
right: null
},
right: {
value: 2,
left: null,
right: null
}
}
and
t2 = {
value: 2,
left: {
value: 1,
left: null,
right: null
},
right: null
}
the output should be isSubtree(t1, t2) = false.
Input/Output
[time limit] 4000ms (rb)
[input] tree.integer t1
A binary tree of integers.
Guaranteed constraints:
0 ≤ tree size ≤ 6 · 104,
-1000 ≤ node value ≤ 1000.
[input] tree.integer t2
Another binary tree of integers.
Guaranteed constraints:
0 ≤ tree size ≤ 6 · 104,
-1000 ≤ node value ≤ 1000.
[output] boolean
Return true if t2 is a subtree of t1, otherwise return false.
DOC
describe "#subtree?" do
# (1(2(),3())
def to_sexpression(tree)
return "()" if tree.nil?
"(#{tree.value}#{to_sexpression(tree.left)},#{to_sexpression(tree.right)})"
end
def subtree?(t1, t2)
return true if (t1.nil? && t2.nil?) || (t1 && t2.nil?)
to_sexpression(t1).include?(to_sexpression(t2))
end
null = nil
[
{ t1: { value: 5, left: { value: 10, left: { value: 4, left: { value: 1, left: null, right: null }, right: { value: 2, left: null, right: null } }, right: { value: 6, left: null, right: { value: -1, left: null, right: null } } }, right: { value: 7, left: null, right: null } }, t2: { value: 10, left: { value: 4, left: { value: 1, left: null, right: null }, right: { value: 2, left: null, right: null } }, right: { value: 6, left: null, right: { value: -1, left: null, right: null } } }, x: true },
{ t1: { value: 5, left: { value: 10, left: { value: 4, left: { value: 1, left: null, right: null }, right: { value: 2, left: null, right: null } }, right: { value: 6, left: { value: -1, left: null, right: null }, right: null } }, right: { value: 7, left: null, right: null } }, t2: { value: 10, left: { value: 4, left: { value: 1, left: null, right: null }, right: { value: 2, left: null, right: null } }, right: { value: 6, left: null, right: { value: -1, left: null, right: null } } }, x: false },
{ t1: { value: 1, left: { value: 2, left: null, right: null }, right: { value: 2, left: null, right: null } }, t2: { value: 2, left: { value: 1, left: null, right: null }, right: null }, x: false },
{ t1: { value: 1, left: { value: 2, left: null, right: null }, right: { value: 2, left: null, right: null } }, t2: null, x: true },
{ t1: null, t2: null, x: true },
{ t1: null, t2: { value: 2, left: null, right: null }, x: false },
{ t1: { value: 1, left: { value: 2, left: null, right: null }, right: { value: 2, left: null, right: null } }, t2: { value: 2, left: null, right: null }, x: true },
{ t1: { value: 3, left: { value: 1 }, right: {} }, t2: null, x: true },
{ t1: { value: 2, right: { value: 3 } }, t2: { value: 2, left: { value: 1 }, right: { value: 3 } }, x: false },
].each do |x|
<<-DOC
2
\
3
2
/ \
1 3
DOC
it do
expect(
subtree?(Tree.build_from(x[:t1]), Tree.build_from(x[:t2]))
).to eql(x[:x])
end
end
end
|
